摘要: Catalan数是指通项公式为
的序列中的
这些数，其最早是由我国清代数学家明安图开始研究的。本文运用Catalan数与生成函数法来解决一类特殊数学结构的计数问题，构造出该数学结构解个数的显性表达式。最后还给出了该数学结构计数问题的另一种解决方案，从另一个角度也利用了广义的Catalan数来解决问题。
Abstract:
Catalan number is an important counting function in the combination of a counting theory. It’s general formula:
. It was first used by the mathematician Antu in Qing dynasty. The paper uses the method of Catalan number and generating function to solve a class of problems counting the special mathematical structure and constructs the explicit expression of the solution of the mathematical structure. Finally, the paper gives another solution of the mathematical structure counting problem and also makes use of generalized Catalan number from another angle to solve the problem.